Ligand-induced conformational change of a protein reproduced by a linear combination of displacement vectors obtained from normal mode analysis

The conformational change of a protein upon ligand binding was examined by normal mode analysis (NMA) based on an elastic-network model (ENM) for a full-atom system using dihedral angles as independent variables. Specifically, we investigated the extent to which conformational change vectors of atoms from an apo form to a holo form of a protein can be represented by a linear combination of the displacement vectors of atoms in the apo form calculated for the lowest-frequency m normal modes (m=1, 2,…, 20). In this analysis, the latter vectors were best fitted to the former ones by the least-squares method. Twenty-two paired proteins in the holo and apo forms, including three dimer pairs, were examined. The results showed that, in most cases, the conformational change vectors were reproduced well by a linear combination of the displacement vectors of a small number of low-frequency normal modes. The conformational change around an active site was reproduced as well as the entire conformational change, except for some proteins that only undergo significant conformational changes around active sites. The weighting factors for 20 normal modes optimized by the least-squares fitting characterize the conformational changes upon ligand binding for these proteins. The conformational changes sampled around the apo form of a protein by the linear combination of the displacement vectors obtained by ENM-based NMA may help solve the flexible-docking problem of a protein with another molecule because the results presented herein suggest that they have a relatively high probability of being involved in an actual conformational change.     

Mechanical property of a TIM-barrel protein

The mechanical response of a TIM-barrel protein to an applied pressure has been studied. We generated structures under an applied pressure by assuming the volume change to be a linear function of normal mode variables. By Delaunay tessellation, the space occupied by protein atoms is divided uniquely into tetrahedra, whose four vertices correspond to atomic positions. Based on the atoms that define them, the resulting Delaunay tetrahedra are classified as belonging to various secondary structures in the protein. The compressibility of various regions identified with respect to secondary structural elements in this protein is obtained from volume changes of respective regions in two structures with and without an applied pressure. We found that the β barrel region located at the core of the protein is quite soft. The interior of the β barrel, occupied by side chains of β strands, is the softest. The helix, strand, and loop segments themselves are extremely rigid, while the regions existing between these secondary structural elements are soft. These results suggest that the regions between secondary structural elements play an important role in protein dynamics. Another aspect of tetrahedra, referred to as bond distance, is introduced to account for rigidities of the tetrahedra. Bond distance is a measure of separation of the atoms of a tetrahedron in terms of number of bonds along the polypeptide chain or side chains. Tetrahedra with longer bond distances are found to be softer on average. From this behavior, we derive a simple empirical equation, which well describes the compressibilities of various regions. © 1997 Wiley-Liss Inc.     

Normal mode analysis of mouse epidermal growth factor: Characterization of the harmonic motion

Normal mode analysis of mouse epidermal growth factor (mEGF) has been carried out at room temperature. The value of the lowest frequency is 4.1 cm^?1. This mode corresponds to hinge-bending motion between the N-terminal and C-terminal domains of mEGF. This hinge-bending motion corresponds to the “mitten mode.” In this motion, the N-terminal domain is almost rigid. However, the C-terminal domain is found to consist of three rigid segments. Two segments, C33-D46 and G51-R53, are observed moving in the same direction, but L47-W50 moves in the opposite direction. For this mode, the effective Young's modulus turned out to be 1.1 × 10⁹ dyn·^?2. This value is a little larger than that of the mode with the lowest frequency 4.4 cm^?1 of BPTI. The difference may be related to the fraction of residues involved in β-sheets in the molecule. Similar analyses are carried out for other low frequency modes.     

ATP-Induced phosphorylation of the sarcoplasmic reticulum Ca2+ ATPase: molecular interpretation of infrared difference spectra.

Time-resolved infrared difference spectra of the ATP-induced phosphorylation of the sarcoplasmic reticulum Ca2+-ATPase have been recorded in H2O and 2H2O at pH 7.0 and 1 degrees C. The reaction was induced by ATP release from P3-1-(2-nitro)phenylethyladenosine 5'-triphosphate (caged ATP) and from [gamma-18O3]caged ATP. A band at 1546 cm-1, not observed with the deuterated enzyme, can be assigned to the amide II mode of the protein backbone and indicates that a conformational change associated with ATPase phosphorylation takes place after ATP binding. This is also indicated between 1700 and 1610 cm-1, where bandshifts of up to 10 cm-1 observed upon protein deuteration suggest that amide I modes of the protein backbone dominate the difference spectrum. From the band positions it is deduced that alpha-helical, beta-sheet, and probably beta-turn structures are affected in the phosphorylation reaction. Model spectra of acetyl phosphate, acetate, ATP, and ADP suggest the tentative assignment of some of the bands of the phosphorylation spectrum to the molecular groups of ATP and Asp351, which participate directly in the phosphate transfer reaction: a positive band at 1719 cm-1 to the C==O group of aspartyl phosphate, a negative band at 1239 cm-1 to the nuas(PO2-) modes of the bound ATP molecule, and a positive band at 1131 cm-1 to the nuas(PO32-) mode of the phosphoenzyme phosphate group, the latter assignment being supported by the band's sensitivity toward isotopic substitution in the gamma-phosphate of ATP. Band positions and shapes of these bands indicate that the alpha- and/or beta-phosphate(s) of the bound ATP molecule become partly dehydrated when ATP binds to the ATPase, that the phosphoenzyme phosphate group is unprotonated at pH 7.0, and that the C==O group of aspartyl phosphate does not interact with bulk water. The Ca2+ binding sites seem to be largely undisturbed by the phosphorylation reaction, and a functional role of the side chains of Asn, Gln, and Arg residues was not detected.     

Normal modes for predicting protein motions: a comprehensive database assessment and associated Web tool

We carry out an extensive statistical study of the applicability of normal modes to the prediction of mobile regions in proteins. In particular, we assess the degree to which the observed motions found in a comprehensive data set of 377 nonredundant motions can be modeled by a single normal-mode vibration. We describe each motion in our data set by vectors connecting corresponding atoms in two crystallographically known conformations. We then measure the geometric overlap of these motion vectors with the displacement vectors of the lowest-frequency mode, for one of the conformations. Our study suggests that the lowest mode contains useful information about the parts of a protein that move most (i.e., have the largest amplitudes) and about the direction of this movement. Based on our findings, we developed a Web tool for motion prediction (available from http://molmovdb.org/nma) and apply it here to four representative motions--from bacteriorhodopsin, calmodulin, insulin, and T7 RNA polymerase.     

Deoxymyoglobin studied by the conformational normal mode analysis. II. The conformational change upon oxygenation

The conformational change taking place in myoglobin concomitantly with the observed geometrical change at the heme-His(F8) linkage upon oxygenation is studied by normal mode analysis, which is based on the quadratic approximation of the conformational energy function. The heme-globin interaction energy increases for this change by 8.114 kcal/mol when both the heme group and the globin molecule are held rigid. When they are permitted flexibility, the interaction energy relaxes by 7.038 kcal/mol, and the difference (1.076 kcal/mol) is distributed as strain energy within the molecule. This increase is the work necessary for the heme group to move against the force exerted by the globin. If the force is assumed to be invariable during this move, the work is small, 0.276 kcal/mol, meaning that the force is strongly variable. Furthermore, this means that the heme group is located near the equilibrium point of the potential energy of the heme-globin interaction. The change in the localized strain energy stored in the force field at the linkage between the heme and the imidazole of HisF8 is estimated to be of the same order of magnitude as the distributed energy. The largest atomic displacements are observed at the region from the F helix to the beginning of the G helix, and secondary large displacements occur at several regions, i.e, the A helix, from the C helix to the CD corner, the E helix, and the C-terminal side of the H helix. All of these regions have strong dynamic interactions with the heme group, either directly or indirectly. Their secondary structures show complex deformations. In other parts, relatively rigid segments undergo rotational and/or bending changes in a way consistent with the large changes described above and close atomic packing within the molecule. The calculated conformational change is decomposed to vibrational normal modes of deoxymyoglobin. The magnitude of the conformational change, measured by the mass-weighted mean-square atomic displacement, is accounted for up to 92.0% by the 151 normal modes with frequencies lower than 40 cm-1. In descending order of contribution, the first six modes, each of which has a frequency lower than 12 cm-1, account for up to 57.4%. This means that the functionally important conformational change can well be expressed in terms of a relatively small number of collective low frequency normal modes.     

A Raman study of low frequency intrahelical modes in A-, B-, and C-DNA.

We have obtained low frequency (less than 200 cm-1) Raman spectra of calf-thymus DNA and poly(rI).poly(rC) as a function of water content and counterion species and of d(GGTATACC)2 and d(CGCGAATTCGCG)2 crystals. We have found that the Raman scattering from water in the first and second hydration shells does not contribute directly to the Raman spectra of DNA. We have determined the number of strong Raman active modes by comparing spectra for different sample orientations and polarizations and by obtaining fits to the spectra. We have found at least five Raman active modes in the spectra of A- and B-DNA. The frequencies of the modes above 40 cm-1 do not vary with counterion species, and there are only relatively small changes upon hydration. These modes are, therefore, almost completely internal. The mode near 34 cm-1 in A-DNA is mostly internal, whereas the mode near 25 cm-1 is dominated by interhelical interactions. The observed intensity changes upon dehydration were found to be due to the decrease in interhelical distance. Polymer length appears to play a role in the lowest frequency modes.     

Rapid protein-ligand docking using soft modes from molecular dynamics simulations to account for protein deformability: binding of FK506 to FKBP

Most current docking methods to identify possible ligands and putative binding sites on a receptor molecule assume a rigid receptor structure to allow virtual screening of large ligand databases. However, binding of a ligand can lead to changes in the receptor protein conformation that are sterically necessary to accommodate a bound ligand. An approach is presented that allows relaxation of the protein conformation in precalculated soft flexible degrees of freedom during ligand-receptor docking. For the immunosuppressant FK506-binding protein FKBP, the soft flexible modes are extracted as principal components of motion from a molecular dynamics simulation. A simple penalty function for deformations in the soft flexible mode is used to limit receptor protein deformations during docking that avoids a costly recalculation of the receptor energy by summing over all receptor atom pairs at each step. Rigid docking of the FK506 ligand binding to an unbound FKBP conformation failed to identify a geometry close to experiment as favorable binding site. In contrast, inclusion of the flexible soft modes during systematic docking runs selected a binding geometry close to experiment as lowest energy conformation. This has been achieved at a modest increase of computational cost compared to rigid docking. The approach could provide a computationally efficient way to approximately account for receptor flexibility during docking of large numbers of putative ligands and putative docking geometries.     

Flexibility of alpha-helices: results of a statistical analysis of database protein structures

Alpha-helices stand out as common and relatively invariant secondary structural elements of proteins. However, alpha-helices are not rigid bodies and their deformations can be significant in protein function (e.g. coiled coils). To quantify the flexibility of alpha-helices we have performed a structural principal-component analysis of helices of different lengths from a representative set of protein folds in the Protein Data Bank. We find three dominant modes of flexibility: two degenerate bend modes and one twist mode. The data are consistent with independent Gaussian distributions for each mode. The mode eigenvalues, which measure flexibility, follow simple scaling forms as a function of helix length. The dominant bend and twist modes and their harmonics are reproduced by a simple spring model, which incorporates hydrogen-bonding and excluded volume. As an application, we examine the amount of bend and twist in helices making up all coiled-coil proteins in SCOP. Incorporation of alpha-helix flexibility into structure refinement and design is discussed.     

Raman and infrared spectroscopy of the oxo-bridged iron(III) complex, [Cl3Fe-O-FeCl3]-2 as a spectroscopic model for the oxo bridge in hemerythrin and ribonucleotide reductase

Vibrational spectroscopic data were collected on the salt [C5H6N]2[Cl3FeOFeCl3] . C5H5N, which has previously been structurally characterized by X-ray crystallography. The modes associated with the oxo bridge were identified by experiments on the 18O-containing species. Spectra for the mu-16O complex contain Raman bands at 870, 458, and 203 cm-1 that shift to 826, 440, and 198 cm-1 in the mu-18O complex. These are respectively assigned to the asymmetric, symmetric, and angle deformations of the bent Fe-O-Fe moiety. A normal mode vibration analysis based on a simple valence force field for the Fe-O-Fe portion of the molecule provides surprisingly good agreement with these experimental frequencies and their assignments. The vibrational data for this simple inorganic complex confirm the assignment of a resonance Raman band around 500 cm-1 in the oxygen-carrying protein hemerythrin and enzyme ribonucleotide reductase as the symmetric stretch of an oxo bridge between two iron(III) centers.     

Approximation and visualization of large-scale motion of protein surfaces

We present a method for the approximation and real-time visualization of large-scale motion of protein surfaces. A molecular surface is represented by an expansion of spherical harmonic functions, and the motion of protein atoms around their equilibrium positions is computed by normal mode analysis. The motion of the surface is approximated by projecting the normal mode vectors of the solvent-accessible atoms to the spherical harmonic representation of the molecular surface. These surface motion vectors are represented by a separated spherical harmonic expansion. Representing the surface geometry and the surface motion vectors by spherical harmonic expansions allows variable-resolution analysis and real-time display of the large-scale surface motion. This technique has been applied to interactive visualization, interactive surface manipulation, and animation.     

Resonance Raman spectra of plastocyanin and pseudoazurin: evidence for conserved cysteine ligand conformations in cupredoxins (blue copper proteins)

New resonance Raman (RR) spectra at 15 K are reported for poplar (Populus nigra) and oleander (Oleander nerium) plastocyanins and for Alcaligenes faecalis pseudoazurin. The spectra are compared with those of other blue copper proteins (cupredoxins). In all cases, nine or more vibrational modes between 330 and 460 cm-1 can be assigned to a coupling of the Cu-S(Cys) stretch with Cys ligand deformations. The fact that these vibrations occur at a relatively constant set of frequencies is testimony to the highly conserved ground-state structure of the Cu-Cys moiety. Shifts of the vibrational modes by 1-3 cm-1 upon deuterium exchange can be correlated with N-H...S hydrogen bonds from the protein backbone to the sulfur of the Cys ligand. There is marked variability in the intensities of these Cys-related vibrations, such that each class of cupredoxin has its own pattern of RR intensities. For example, plastocyanins from poplar, oleander, French bean, and spinach have their most intense feature at approximately 425 cm-1; azurins show greatest intensity at approximately 410 cm-1, stellacyanin and ascorbate oxidase at approximately 385 cm-1, and nitrite reductase at approximately 360 cm-1. These variable intensity patterns are related to differences in the electronic excited-state structures. We propose that they have a basis in the protein environment of the copper-cysteinate chromophore. A further insight into the vibrational spectra is provided by the structures of the six cupredoxins for which crystallographic refinements at high resolution are available (plastocyanins from P. nigra, O. nerium, and Enteromorpha prolifera, pseudoazurin from A. faecalis, azurin from Alcaligenes denitrificans, and cucumber basic blue protein). The average of the Cu-S(Cys) bond lengths is 2.12 +/- 0.05 A. Since the observed range of bond lengths falls within the precision of the determinations, this variation is considered insignificant. The Cys ligand dihedral angles are also highly conserved. Cu-S gamma-C beta-C alpha is always near -170 degrees and S gamma-C beta-C alpha-N near 170 degrees. As a result, the Cu-S gamma bond is coplanar with the Cys side-chain atoms and part of the polypeptide backbone. The coplanarity accounts for the extensive coupling of Cu-S stretching and Cys deformation modes as seen in the RR spectrum. The conservation of this copper-cysteinate conformation in cupredoxins may indicate a favored pathway for electron transfer.     

Multiscale modeling of macromolecular conformational changes combining concepts from rigidity and elastic network theory

The development of a two-step approach for multiscale modeling of macromolecular conformational changes is based on recent developments in rigidity and elastic network theory. In the first step, static properties of the macromolecule are determined by decomposing the molecule into rigid clusters by using the graph-theoretical approach FIRST and an all-atom representation of the protein. In this way, rigid clusters are not limited to consist of residues adjacent in sequence or secondary structure elements as in previous studies. Furthermore, flexible links between rigid clusters are identified and can be modeled as such subsequently. In the second step, dynamical properties of the molecule are revealed by the rotations-translations of blocks approach (RTB) using an elastic network model representation of the coarse-grained protein. In this step, only rigid body motions are allowed for rigid clusters, whereas links between them are treated as fully flexible. The approach was tested on a data set of 10 proteins that showed conformational changes on ligand binding. For efficiency, coarse-graining the protein results in a remarkable reduction of memory requirements and computational times by factors of 9 and 27 on average and up to 25 and 125, respectively. For accuracy, directions and magnitudes of motions predicted by our approach agree well with experimentally determined ones, despite embracing in extreme cases >50% of the protein into one rigid cluster. In fact, the results of our method are in general comparable with when no or a uniform coarse-graining is applied; and the results are superior if the movement is dominated by loop or fragment motions. This finding indicates that explicitly distinguishing between flexible and rigid regions is advantageous when using a simplified protein representation in the second step. Finally, motions of atoms in rigid clusters are also well predicted by our approach, which points to the need to consider mobile protein regions in addition to flexible ones when modeling correlated motions.     

Dynamics of transfer RNAs analyzed by normal mode calculation.

Normal mode calculation is applied to tRNAPhe and tRNAAsp, and their structural and vibrational aspects are analyzed. Dihedral angles along the phosphate-ribose backbone (alpha, beta, gamma, epsilon, zeta) and dihedral angles of glycosyl bonds (chi) are selected as movable parameters. The calculated displacement of each atom agrees with experimental data. In modes with frequencies higher than 130 cm-1, the motions are localized around each stem and the elbow region of the L-shape. On the other hand, collective motions such as bending or twisting of arms are seen in modes with lower frequencies. Hinge axes and bend angles are calculated without prior knowledge. Movements in modes with very low frequencies are combinations of hinge bending motions with various hinge axes and bend angles. The thermal fluctuations of dihedral angles well reflect the structural characters of transfer RNAs. There are some dihedral angles of nucleotides located around the elbow region of L-shape, which fluctuate about five to six times more than the average value. Nucleotides in the position seem to be influential in the dynamics of the entire structure. The normal mode calculation seems to provide much information for the study of conformational changes of transfer RNAs induced by aminoacyl-tRNA synthetase or codon during molecular recognition.     

Resonance Raman studies of Escherichia coli sulfite reductase hemoprotein. 2. Fe4S4 cluster vibrational modes

Resonance Raman (RR) spectra from the hemoprotein subunit of Escherichia coli sulfite reductase (SiR-HP) are examined in the low-frequency (200-500 cm-1) region where Fe-S stretching modes are expected. In spectra obtained with excitation in the siroheme Soret or Q bands, this region is dominated by siroheme modes. Modes assignable to the Fe4S4 cluster are selectively enhanced, however, with excitation at 488.0 or 457.9 nm. The assignments are confirmed by observation of the expected frequency shifts in SiR-HP extracted from E. coli grown on 34S-labeled sulfate. The mode frequencies and isotopic shifts resemble those seen in RR spectra of other Fe4S4 proteins and analogues, but the breathing mode of the cluster at 342 cm-1 is higher than that observed in the other species. Spectra of various ligand complexes of SiR-HP reveal only slight sensitivity of the cluster terminal ligand modes to the presence of exogenous heme ligands, at variance with a model of ligand binding in a bridged mode between heme and cluster. Close examination of RR spectra obtained with siroheme Soret-band excitation reveals additional 34S-sensitive features at 352 and 393 cm-1. These may be attributed to a bridging thiolate ligand.     

Dynamic and structural analysis of isotropically distributed molecular ensembles.

An efficient new method is presented for the characterization of motional correlations derived from a set of protein structures without requiring the separation of overall and internal motion. In this method, termed isotropically distributed ensemble (IDE) analysis, each structure is represented by an ensemble of isotropically distributed replicas corresponding to the situation found in an isotropic protein solution. This leads to a covariance matrix of the cartesian atomic positions with elements proportional to the ensemble average of scalar products of the position vectors with respect to the center of mass. Diagonalization of the covariance matrix yields eigenmodes and amplitudes that describe concerted motions of atoms, including overall rotational and intramolecular dynamics. It is demonstrated that this covariance matrix naturally distinguishes between "rigid" and "mobile" parts without necessitating a priori selection of a reference structure and an atom set for the orientational alignment process. The method was applied to the analysis of a 5-ns molecular dynamics trajectory of native ubiquitin and a 40-ns trajectory of a partially folded state of ubiquitin. The results were compared with essential dynamics analysis. By taking advantage of the spherical symmetry of the IDE covariance matrix, more than a 10-fold speed up is achieved for the computation of eigenmodes and mode amplitudes. IDE analysis is particularly suitable for studying the correlated dynamics of flexible and large molecules.     

Low frequency Raman spectra of Z-DNA

We have performed a Raman study of the low frequency modes in three oligo- and polynucleotides in Z-conformation, and we compare the spectra of these samples to those of two polynucleotides in B-conformation. In Z-DNA we find 5 intrahelical modes below 200 cm-1, in addition to the interhelical mode near 30 cm-1 which is only observed in crystalline samples. The most prominent intrahelical mode has a frequency of about 105 cm-1, close to the frequency of the strongest intrahelical mode in A-and B-DNA. The sequence dependence of the frequency of this mode is considerably larger than for the same mode in B-DNA. The other modes are less pronounced, and their frequency variations with base sequence are within the experimental accuracy.     

Direct measurement of hydration-related dynamic changes in lysozyme using inelastic neutron scattering spectroscopy

Inelastic neutron scattering spectroscopy is used to investigate dynamic changes in lysozyme powder at two different low D2O hydrations (0.07g D2O/g protein and 0.20 g D2O/g protein). In the higher hydration sample, the inelastic scattering between 0.8 and 4.0 cm-1 energy transfer is increased and the elastic scattering is decreased. The decreased elastic scattering suggests increased atomic amplitudes of motion and the increased 0.8 to 4.0 cm-1 scattering suggests increased motions in this frequency range. Comparison with normal mode models of lysozyme dynamics shows that the inelastic difference occurs in the frequency region predicted for the lowest frequency, largest amplitude, global modes of the molecular [M. Levitt, C. Sander and P.S. Stern, J. Mol. Biol. 181, 423 (1985). B. Brooks and M. Karplus, Proc. Natl. Acad. Sci (U.S.A) 82, 4995 (1985), R.E. Bruccoleri, M. Karplus and J.A. McCammon, Biopolymers 25 1767 (1986)]. Our results are consistent with a model in which an increased number of low frequency global modes are present in the higher hydrated sample.